A semiclassical model is used to perform numerical simulations of the production of nuclear fragments in both proton- and heavy-ion-induced reactions. The Pauli principle is incorporated by means of a collision term, as it is in the Vlasov-Uehling-Uhlenbeck equation. The model goes beyond the Vlasov-Uehling-Uhlenbeck equation by propagating on an event-by-event basis the phase space fluctuations which develop during a nuclear reaction. Both the Coulomb and isospin-dependent interaction terms are included. For proton-induced reactions at intermediate energies, fragment production is found to be a fairly infrequent process, as is observed experimentally. Heavy-ion reactions show much greater fragment yields. For these latter reactions, we have compiled sufficiently many events so as to be able to compare the predicted fragment yields with experiment. The isotopic distribution of products, as well as their distribution in momentum space, are also examined. The events are used to generate a two-particle correlation function. Analysis of the energy-summed two-proton correlations indicates a large source region. The coordinate and phase space reaction trajectories are followed for a central collision, and preliminary evidence is found in the simulations for the onset of mechanical instability.